A number of systems and programs are offered on the market for the design, the engineering and the manufacturing of objects. CAD is an acronym for Computer-Aided Design, e.g. it relates to software solutions for designing an object. CAE is an acronym for Computer-Aided Engineering, e.g. it relates to software solutions for simulating the physical behavior of a future product. CAM is an acronym for Computer-Aided Manufacturing, e.g. it relates to software solutions for defining manufacturing processes and operations. In such computer-aided design systems, the graphical user interface plays an important role as regards the efficiency of the technique. These techniques may be embedded within Product Lifecycle Management (PLM) systems. PLM refers to a business strategy that helps companies to share product data, apply common processes, and leverage corporate knowledge for the development of products from conception to the end of their life, across the concept of extended enterprise.
The PLM solutions provided by DASSAULT SYSTEMES (under the trademarks CATIA, ENOVIA and DELMIA) provide an Engineering Hub, which organizes product engineering knowledge, a Manufacturing Hub, which manages manufacturing engineering knowledge, and an Enterprise Hub which enables enterprise integrations and connections into both the Engineering and Manufacturing Hubs. All together the system delivers an open object model linking products, processes, resources to enable dynamic, knowledge-based product creation and decision support that drives optimized product definition, manufacturing preparation, production and service.
CAD often involves surfaces for representing 3D modeled objects. Surface modeling is used notably in styling design, including class A design, where motivations include the aesthetic aspect of a manufactured product. Typical surfaces are provided by the mathematics of Bezier, B-Spline and more generally NURBS (non-uniform rational B-spline) curves and surfaces models. All these models provide the very popular concept of “control points”. The surface is defined by a grid of points and moving these points appropriately changes the shape of the surface. Typical references are:                The NURBS book, L. Piegl, W. Tiler, Springer Science, 1997; and        Curves and surfaces for computer aided geometric design: a practical guide, G. Farin, Hardcover, 1996.        
Existing systems aim at allowing easy interactive manipulations by the user, for modification of the surface. By definition, an easy manipulation is intuitive and predictable, meaning that a beginner rapidly understands how to change the shape of a surface and that a skilled user can anticipate the surface resulting from the manipulation.
Some methods for shaping NURBS surfaces involve geometric constraints or physical behavior. Geometric constraints methods compute new control points so that the deformed surface meets the user defined geometry (point, set of points, curve). Physical behavior is for the user to apply forces on the surface that behaves like an elastic material. References include:                Dynamic NURBS with Geometric Constraints for Interactive Sculpting, D. Terzopoulos, H. Qin, ACM Transactions on Graphics, 13(2), April 1994, 103-136; and        Modifying the shape of NURBS surfaces with geometric constraints, S. M. Hu, Y. F. Li, T. Ju, X. Zhu, Computer Aided Design, 33 (2001) 903-912.        
Within this context, there is still a need for an improved solution to design a 3D modeled object.